Compare Products

10 min

Narrative

The purpose of this True or False? is for students to demonstrate strategies they have to estimate the size of a product. Students can find the value of 45×100\frac{4}{5} \times 100 and thereby solve all of the problems, but the exact value is not needed to make the comparisons. Throughout the next several lessons, students will investigate different ways to compare a product such as this to one of its factors (100 in this case).

Launch

  • Display the first statement.
  • “Give me a signal when you know whether the equation or inequality is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record students’ answers and strategies.
  • Repeat with each equation.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 45×100=120\frac{4}{5} \times 100 = 120
  • 45×100<100\frac{4}{5} \times 100 < 100
  • 45×100=80\frac{4}{5} \times 100 = 80

Sample Response

  • False: 45\frac{4}{5} of 100 is less than 100, so it can’t be 120.
  • True: 45\frac{4}{5} is less than 1 whole, so 45\frac{4}{5} of 100 is less than 100.
  • True: 15\frac{1}{5} of 100 is 20 and 4×20=804 \times 20 = 80.

Synthesis

  • Display: 45×100<100\frac{4}{5} \times 100 < 100
  • “How do we know this is true, without finding the value of 45×100\frac{4}{5}\times100?” (Since 45\frac{4}{5} is 15\frac{1}{5} less than 1 whole, 45×100\frac{4}{5} \times 100 is less than 1×1001 \times 100. I know that 45×100\frac{4}{5} \times 100 is 80, and that's less than 100.)
Standards
Building Toward
  • 5.NF.5.a·Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
  • 5.NF.B.5.a·Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

15 min

20 min